Question: 1. 2. 3. 4. 5. 6. Determine whether each function is convex, concave or neither. f(x) = ex + x4 f(x, y) = x

1. 2. 3. 4. 5. 6. Determine whether each function is convex,

1. 2. 3. 4. 5. 6. Determine whether each function is convex, concave or neither. f(x) = ex + x4 f(x, y) = x + 3xy + y a. b. Find the values of a, b, and c such that f(x, y) = ax + bxy + cy is a concave function Use the following function to construct a convex set z = x + ey By drawing sketches, decide if the sets {(x, y) = R y x} are convex or not A company produces two goods sold in two separate markets, where P = 200-40 - 3Qz P = 230-501 - 202 TC = 2Q1 +2Q1 Q + 4Q/ Total profit: = (PQ + PQ) - TC Find values of Q1 and Q2 where total profit is maximized and check the second order condition One firm producing 3 goods under perfect competition: TR = P1Q1 + PQ2 + P3Q3 TC = Q + Q + Q3 Find profit maximizing quantity of good 1 and good 2, good 3. Check that they satisfy the maximum condition. a. b.

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1 Determine whether each function is convex concave or neither a To determine the convexity of fx e2x x we need to check the second derivative fx ddxe2x x ddx2e2x 1 4e2x Since fx 4e2x is positive for ... View full answer

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